Quality and the diffusion of innovations

In this paper, we solve the problem of optimal control of products diffusion by quality in a context of monopolistic competition. To do so, we introduce a dynamic demand function leaning on two hypotheses: first, price acts as a signal of quality; second, demand is more sensitive to quality than to price. Using the maximum principle of Pontryagin, we then characterize the optimal dynamic trajectory of quality and its qualitative properties.